Dirichlet conditions guarantee that a periodic function can be exactly represented by its Fourier transform.
The function must be absolutely integrable over a single period . This is equivalent to the statement that the area enclosed between the abcissa and the function is finite over a single period.
Given any finite period of time the number of local maxima and minima of within that period is finite.
Given any finite period of time there is a finite number of discontinuities in the function